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3- Determine the centroid for the sections shown. 8 cm

3- Determine the centroid for the sections shown. 8 cm

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Determine the Centroid for the Sections Shown** The diagram depicts a composite geometric shape divided into sections that form an irregular outline. The shape can be analyzed as follows: 1. **Coordinate Axes**: - The x-axis is horizontal, and the y-axis is vertical. - The point where the axes intersect is the origin (0,0). 2. **Dimensions**: - The base of the shape spans from 0 cm to 6 cm along the x-axis. - The height of the shape can be split into two levels: - The first level starts at the y-axis and ends at 2 cm on the x-axis, with a height of 5 cm. - The second level continues from x = 2 cm to x = 4 cm with an extended height of 8 cm. 3. **Outline**: - The shape is composed of a rectangle on the left and a trapezoidal section on the right. - The rectangle forms a vertical from the origin up to a point marked as 5 cm on the y-axis. - It extends horizontally till x = 2 cm, meeting at a height of 8 cm, and then slopes down to meet the x-axis at x = 6 cm. The goal is to calculate the centroid of this shape by dividing it into simpler geometric sections (e.g., rectangles and a trapezoid) and then using the formula for centroids of these shapes to find the overall centroid of the composite shape.
Transcribed Image Text:**Determine the Centroid for the Sections Shown** The diagram depicts a composite geometric shape divided into sections that form an irregular outline. The shape can be analyzed as follows: 1. **Coordinate Axes**: - The x-axis is horizontal, and the y-axis is vertical. - The point where the axes intersect is the origin (0,0). 2. **Dimensions**: - The base of the shape spans from 0 cm to 6 cm along the x-axis. - The height of the shape can be split into two levels: - The first level starts at the y-axis and ends at 2 cm on the x-axis, with a height of 5 cm. - The second level continues from x = 2 cm to x = 4 cm with an extended height of 8 cm. 3. **Outline**: - The shape is composed of a rectangle on the left and a trapezoidal section on the right. - The rectangle forms a vertical from the origin up to a point marked as 5 cm on the y-axis. - It extends horizontally till x = 2 cm, meeting at a height of 8 cm, and then slopes down to meet the x-axis at x = 6 cm. The goal is to calculate the centroid of this shape by dividing it into simpler geometric sections (e.g., rectangles and a trapezoid) and then using the formula for centroids of these shapes to find the overall centroid of the composite shape.
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